Ancient geometry dates back to around 3000 BC, and constitutes one of the earliest advances in geometry. It began in Europe when the Egyptians used it in many ways, including land surveying, pyramid building, and astronomy. The next advance came from the Babylonians between 2000 and 500 BC. Ancient clay tablets showed that the Babylonians knew of Pythagorean relationships. Say no to plagiarism. Get a tailor-made essay on “Why Violent Video Games Should Not Be Banned”? Get the original essay Between 750 and 250 BC, the Greeks practiced experimental geometry as did Egypt and Babylonia. They created the first formal mathematics of any kind by organizing geometry with rules of logic. The next advancement in Euclid's geometry game. In 300 BC he wrote a text called “Elements”. This stated that ideas could be proven through a small set of statements (postulates). The five postulates were as follows: A straight line segment can be drawn joining any two points. Given any straight line segment, a circle can be drawn having the segment as the radius and an end point as the center. All right angles are congruent. If two lives are drawn which intersect a third line such that the sum of the interior angles, then the two lines must inevitably intersect on the side if extended indefinitely. There has been much controversy over the fifth postulate. The fifth postulate states: “Given a line and a point which does not lie on the line, it is possible to draw exactly a line passing through the given point parallel to the line. » Many mathematicians over the following centuries tried unsuccessfully to prove this postulate. In 1600 AD, René Descartes made one of the greatest advances in geometry. He linked algebra and geometry. One myth is that he was observing a fly on the ceiling when he conceived of locating points on a plane with a pair of numbers. Fermat also discovered coordinate geometry, but Descartes' version is the one we use today. In the early 1800s, Bolyai and Lobachevsky created the first non-Euclidean geometries. Since no one could prove Euclid's fifth postulate, they designed new geometries with "strange" notions of parallelism. From the late 1800s to the early 1900s, Gauss and Riemann laid the foundation for differential geometry. Differential geometry combines geometry with computational techniques to provide a method for studying geometry on curved surfaces. Keep in mind: this is just a sample. Get a personalized article from our expert writers now. Get a Custom Essay Also in the late 1800s and early 1900s Mandelbrot and a few other researchers studied fractal geometry. Fractals are geometric figures that model many natural structures. The invention of computers helped the study of fractals.